How to add modifiers using python script and set parameters?
You can add a new modifier to an object with ObjectModifiers.new(). If you store the result of calling ObjectModifiers.new() in a variable (in the example below I call it modifier) you then have access to all the properties of the new modifier:    

import bpy

object = bpy.data.objects['Cube']

modifier = object.modifiers.new(name="Remesh", type='REMESH')
modifier.octree_depth = 5


You can see the type of modifier by hovering the mouse over the modifier in the Add modifier menu and you can see the name of the properties by hovering over the properties on the modifier.